Related papers: Trace theorems: critical cases and best constants
In this paper, we consider the trace theorem for modulation spaces, alpha modulation spaces and Besov spaces. For the modulation space, we obtain the sharp results.
We investigate the extremal values of partial traces of matrix tensors under operator norm constraints. To evaluate these multi-linear quantities, we develop a comprehensive graphical formalism that encodes multi-leg partial traces, partial…
Our goal is to extend the theory of the spectral shift function to the case where only the difference of some powers of the resolvents of self-adjoint operators belongs to the trace class. As an example, we consider a couple of Dirac…
In order to design and implement tracers, one must decide what exactly to trace and how to produce this trace. On the one hand, trace designs are too often guided by implementation concerns and are not as useful as they should be. On the…
We give asymptotic bounds for the optimal Lipschitz constants for the systole map from the Teichmuller space to the curve complex. We give similar results to those known for closed surfaces in the cases when the genus is fixed or the ratio…
In this paper we address the problem of tracking control of nonlinear systems via contraction analysis. The necessary conditions of the systems which can achieve universal asymptotic tracking are studied under several different cases. We…
Selection of descent direction at a point plays an important role in numerical optimization for minimizing a real valued function. In this article, a descent sequence is generated for the functions with bounded parameters to obtain a…
The main goal of this article is to understand the trace properties of nonlocal minimal graphs in~$\R^3$, i.e. nonlocal minimal surfaces with a graphical structure. We establish that at any boundary points at which the trace from inside…
We provide sufficient conditions under which the difference of the resolvents of two higher-order operators acting in $\R^N$ belongs to trace classes $\cC^p$. We provide explicit estimates on the norm of the resolvent difference in terms of…
The first aim of this paper is to examine some important properties of soft metric spaces. Second is to introduce soft continuous mappings and investigate properties of soft continuous mappings. Third is to prove some fixed point theorems…
In this paper we consider two problems in diagnostics of trapped ion crystals in which an analysis of the ions' collective oscillatory motion yield potentially useful results. When one of the ions in a linear crystal undergoes a collision,…
Locks are a standard mechanism for synchronizing concurrent threads. The standard lock set construction assumes that critical sections are confined to a single thread, and therefore only accounts for locks acquired within that thread.…
For a certain class of discrete metric spaces, we provide a formula for the density of states. This formula involves Dixmier traces and is proven using recent advances in operator theory. Various examples are given of metric spaces for…
The aim of this paper is to introduce new forms of the weak and Omori-Yau maximum principles for linear operators, notably for trace type operators, and show their usefulness, for instance, in the context of PDE's and in the theory of…
Correctness of concurrent objects is defined in terms of safety properties such as linearizability, sequential consistency, and quiescent consistency, and progress properties such as wait-, lock-, and obstruction-freedom. These properties,…
The aim of this short note is to extend the recent variational proof of partial regularity for optimal transport maps to the case of continuous densities.
We consider a functional being a difference of two differentiable convex functionals on a closed ball. Existence and multiplicity of critical points is investigated. Some applications are given.
Previous work in the area of tracing CLP(FD) programs mainly focuses on providing information about control of execution and domain modification. In this paper, we present a trace structure that provides information about additional…
In this paper, problems of optimal control are considered where in the objective function, in addition to the control cost there is a tracking term that measures the distance to a desired stationary state. The tracking term is given by some…
An introduction into the theory of boundary critical phenomena and the application of the field-theoretical renormalization group method to these is given. The emphasis is on a discussion of surface critical behavior at bulk critical points…